Semitopological BL-Algebras and MV -Algebras

Abstract In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology T x on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity a...

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Bibliographic Details
Published inDemonstratio mathematica Vol. 47; no. 3; pp. 522 - 538
Main Authors Zahiri, O., Borzooei, R. A.
Format Journal Article
LanguageEnglish
Published De Gruyter 01.07.2014
Subjects
and phrases semitopology
BL-algebra
MV -algebra
upset
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Summary:Abstract In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology T x on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of MV -algebra and show that they are equivalent.
ISSN:0420-1213
2391-4661
DOI:10.2478/dema-2014-0043